Let G be a finite group, V a complex permutation module for G over a finite G-set 𝒳, and f:V×V→ℂ a G-invariant positive semidefinite hermitian form on V. In this paper we show how to compute the radical V⊥ of f, by extending to nontransitive actions the classical combinatorial methods from the theory of association schemes. We apply this machinery to obtain a result for standard Majorana representations of the symmetric groups.